Planetary astronomy: Rings, satellites, and asteroids

Studies of planetary rings focus on the dynamical processes that govern astronomically observable ring properties and structure. These investigations thus help reveal properties of the rings as well as probe the gravity fields of the planets. Satellite studies involve interpretation of orbital motion to extract information regarding the gravity fields of the outer planets and the physical properties of the satellites themselves. Asteroid lightcurve work is designed to investigate the large-scale shapes of the asteroids, as well as to reveal anomalous features such as major topography, possible satellites, or albedo variations. Work on the nature of viscous transport in planetary rings, emphasizing the role of individual particles' physical properties, has yielded a method for estimating both angular momentum and mass transport given an optical-thickness gradient. This result offers the prospect of ringlet instability, which may explain the square-profile ringlets in Saturn's C Ring. Thermal and reflected lightcurves of 532 Herculina have been interpreted to show that albedo variations cannot be the primary cause of variations. A lightcurve simulation has been developed to model complex asteroidal figures. Bamberga was observed during the December occultation as part of the joint LPL-Lowell program

Stability Limits in Resonant Planetary Systems

The relationship between the boundaries for Hill and Lagrange stability in orbital element space is modified in the case of resonantly interacting planets. Hill stability requires the ordering of the planets to remain constant while Lagrange stability also requires all planets to remain bound to the central star. The Hill stability boundary is defined analytically, but no equations exist to define the Lagrange boundary, so we perform numerical experiments to estimate the location of this boundary. To explore the effect of resonances, we consider orbital element space near the conditions in the HD 82943 and 55 Cnc systems. Previous studies have shown that, for non-resonant systems, the two stability boundaries are nearly coincident. However the Hill stability formula are not applicable to resonant systems, and our investigation shows how the two boundaries diverge in the presence of a mean-motion resonance, while confirming that the Hill and Lagrange boundaries are similar otherwise. In resonance the region of stability is larger than the domain defined by the analytic formula for Hill stability. We find that nearly all known resonant interactions currently lie in this extra stable region, i.e. where the orbits would be unstable according to the non-resonant Hill stability formula. This result bears on the dynamical packing of planetary systems, showing how quantifying planetary systems' dynamical interactions (such as proximity to the Hill-stability boundary) provides new constraints on planet formation models.Comment: 13 pages, 3 figures, 2 tables, accepted for publication in ApJ Letters. A version with full resolution figures is available at http://www.lpl.arizona.edu/~rory/research/xsp/resstab.pd

Simultaneous Equations in the Model System With an Application to Econometric Modelling

This report describes modifications to the MODEL language and processor to facilitate automatic implementation of solution procedures for systems of simultaneous equations. MODEL is a very high level nonprocedural language for specifying computational tasks. The MODEL processor compiles a specification in the MODEL language into a computer program in PL/I . The purpose of the current modifications is to allow users with relatively little programming expertise to solve complex mathematical systems involving sets of simultaneous equations quickly and efficiently using an automatic program generation approach to modelling. The primary application which has motivated these modifications is that of Project LINK, an international econometric model composed of independent constituent country/region models which are linked together into a complex network of simultaneous equations. This report presents the rationale behind these modifications, describes the syntax, semantics, scheduling and code generation of specifications containing simultaneous equations, and illustrates these facilities in applications to two small national models from the LINK system and to a novel linkage mechanism used to simulate trade among the national models

Tidal Effects on the Habitability of Exoplanets: The Case of GJ 581 d

Tides may be crucial to the habitability of exoplanets. If such planets form around low-mass stars, then those in the circumstellar habitable zone will be close enough to their host stars to experience strong tidal forces. Tides may result in orbital decay and circularization, evolution toward zero obliquity, a fixed rotation rate (not necessarily synchronous), and substantial internal heating. Due to tidal effects, the range of habitable orbital locations may be quite different from that defined by the traditional concept of a habitable zone (HZ) based on stellar insolation, atmospheric effects, and liquid water on a planet's surface. Tidal heating may make locations within the traditional HZ too hot, while planets outside the traditional zone could be rendered quite habitable due to tides. Here we consider these effects on the exoplanet GJ 581 d.Comment: 2 pages, 1 figure